Re: average distance between two points in a polygon

I did a simulation choosing N random pairs of points p_i, q_i in a
circle, (square, triangle, respectively) giving distances d_i = |
p_i-q_i |. I add all these distances and divide by N and I get the
following values:

circle, 0.5041293619
square, 0.5153857795
triangle, 0.5489118605

I take each figure to have area 1. The averages vary for different
runs, but the order of magnitude appears to be pretty stable. This is
consistent with Solly's statement.

.

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